The enthalpy of fusion of water is 6.01 kJ/mol. Sunlight striking Earth\'s surfa

Question

The enthalpy of fusion of water is 6.01 kJ/mol. Sunlight striking Earth's surface supplies 168 W per square meter (1 W= 1 watt = 1 J/s.)

a. Assuming that melting of ice is only due to energy input from the Sun, calculate how many grams of ice could be melted from a 1.00 square meter patch of ice over a 12-hour day.

b. The specific heat capacity of ice is 2.032 J/g C. If the initial temperature of a 1.00 square meter patch of ice is -9C, what is its final temperature after being in sunlight for 12 hours, assuming no phase changes and assuming that sunlight penetrates uniformly to a depth of 1.00 cm?

Explanation / Answer

a.) Energy in a day in 1 m2 = P*t

= 168*12*60*60

E = 7257600 J = 7257.6 kJ

Moles of water = 72757.6/6.01 = 1207.59 moles

1 mol of water = 18 g

=> so total weight = 1207.59*18 = 21736.57 g = 21.74 kg

b.) density of ice = 916.7*103 g/m3

( if in your question density of ice is different then substitute that in my solution)

Volume = 1m2*1cm = 1*0.01 = 0.01 m3

Mass of ice = 0.01*916.7*103 = 9167 g

Energy provided = 7257600 J

m*C*T = 7257600

=> 9167*2.032*(T-(-9)) = 7257600

=> T + 9 = 389.62

=> T = 380.62 C ( since its given that there is no phase change)

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